When Anfield swells for a memorial service to mark the 20th anniversary of the Hillsborough disaster today, Liverpool's "mission impossible" against Chelsea in a Champions League quarter-final might look like trivial human theatre. But to trot out the old line about life and death and perspective ignores the reality that for many survivors and relatives of the 96 victims, Liverpool FC have kept a light shining in the dark of sorrow.

A safe guess is that the club and its exploits have felt more, not less, important since nearly 100 Liverpool supporters were crushed to death at Sheffield Wednesday's ground. So for many there was no emotional discrepancy between today's impending ritual on the Kop and the attempt to summon the spirit of Istanbul in London less than 24 hours earlier.

This was a crazy, switchback clash that reaffirmed Liverpool's unique talent for defiance. They scored four at Stamford Bridge and still went out of Europe. Chelsea have conceded seven in their past two home games, yet still advance to a glamour semi-final against Barcelona.

As Liverpool seized a two-goal lead inside 28 minutes, we were back in the remote moonscape of the Ataturk Olympic Stadium, an unlikely setting for a magical transformation. Even as Chelsea recovered their poise to draw level with a goal from Didier Drogba – with a little help from the Liverpool goalkeeper, Pepe Reina – and an Alex free-kick, Liverpool held this tie in their teeth and shook it with late strikes from Lucas and Dirk Kuyt to help create an aggregate of 7-5 in Chelsea's favour.

Three-nil down to AC Milan at half-time in the 2005 Champions League final, Liverpool had scored three in six minutes to present a strong case for the phoenix replacing the Liver bird as their emblem. So fertile are those memories, still, that they were able to rebound from Chelsea's 3-1 victory in last week's first leg with genuine hope that a 100-1 Grand National winner would not be the only shock emanating from Merseyside this spring.

Had the numbingly prosaic Bolton Wanderers not scored three on this very turf when trailing 4-0 on Saturday – the same day Liverpool thumped four past Blackburn Rovers? Those dubious form lines were less luminous on paper than the knowledge that uproarious outcomes are always on the cards when Liverpool appear in European competition, as they did for the 300th time here.

But then the team-sheets dropped, with no sign of the only non-Manchester United player to make the Professional Footballers' Association shortlist for player of the year. Conspiracy theorists wondered whether Steven Gerrard's absence from pitch and bench suggested that Rafa Benítez, his manager, had already consigned this tie to history's dustbin in favour of a concentrated assault on the Premier League title. Nice theory. Then a game broke out to kill it. Chelsea emerged in a stupor as the visitors played the crisper, faster football and began to feed off signs that Guus Hiddink's side might be paralysed by the fear of surrendering such a commanding advantage.

Gerrard had aggravated his groin injury. Into the void left by the hero of Istanbul and countless other big Champions League nights stepped the unheralded Brazilian, Lucas, who earned rare praise from Benítez. Never doubt Brazilian ingenuity. Nineteen minutes in Lucas's compatriot, Aurelio jogged over from left-back to take a free-kick on Chelsea's right flank and curled it past the badly positioned Petr Cech, whose increasing fallibility must be worrying Chelsea's high command. Nine minutes later a penalty conceded by Branislav Ivanovic was converted by Alonso and Liverpool were turning football's world upside down again.

By now it was astonishing to recall the sigh that was let out when these two teams were drawn together for the fifth consecutive season. Was this football or an American dance marathon? As if sensing ennui in the land, the pair contrived to serve up a sparkling 3-1 Chelsea first-leg win and then last night's barn-burner, which produced six second-half goals. There will be no more grumbling if these two come out of the hat together again next year.

For Liverpool's fans, meanwhile, there is the comforting sense that their team's fighting spirit is now more sophisticated than it was in Istanbul, where they triumphed partly because Milan assumed they had already won. The best side assembled by Benítez in his Anfield years have rejoined the Premier League race through the exuberance and ambition of their play, rather than mere stubborn instinct, of which they also have plenty.

"We showed character and quality and we have to be very proud," Benítez said. "We were on top of them from the beginning, credit to all the players, especially Lucas in the middle. In the absence of Gerrard he worked very hard. When you lose in this way you have to be very proud, with your head up. We can win a lot of games with this mentality."

This is the narrow footballing sense that will be shared by the congregation on the Kop today as a two-minute silence commences at 3.06pm. Again, maybe "narrow" is the wrong word, because the game on Merseyside is unquestionably a force for life as well as a spectacle that is indelibly associated with injustice and loss.

After Hillsborough, one would guess, all Liverpool could do was go on beingtrue to themselves, to honour the departed. In this stunning game they achieved that end.

• This article was amended on Thursday 16 April 2009. In the Champions League football report above we said: "As Liverpool seized a two-goal lead inside 28 minutes, we were back in the remote moonscape of the Ataturk Olympic Stadium to the west of Turkey's capital, an unlikely setting for a magical transformation". Magical indeed, as a reader noted, as Ankara is Turkey's capital, not Istanbul where the stadium is. This has been corrected.